Dual coalgebras of alternative and associative bialgebras

M. E. Goncharov<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: In this work we consider dual coalgebras of alternative and associative bialgebras. We prove that the dual coalgebra of an alternative (associative) bialgebra is an alternative (associative) bialgebra.

Keywords: альтернативная алгебра, альтернативная коалгебра, неассоциативная коалгебра, биалгебра Ли, дуальная коалгебра.

UDC: 512.554

MSC: 17D05, 16T15

Received August 18, 2011, published August 22, 2011